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Gravity is not a force – free-fall parabolas are straight lines in spacetime

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Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#191

Post by esc_colon_q »

ncallaway wrote: post #155
abeppu wrote: post #140

I've seen this explained elsewhere, and it does look very cool when displayed this way. But perhaps someone with more background can explain to a lay person -- what even is a force? Why does the existence of a transformation that makes movement under a supposed force actually follow a straight line mean it's not really a force? For the other forces (e.g. electromagnetism) can we say that there's _no way_ to exhibit a…

Newton's first law provides a guide: "Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it." So, the definition of a force as something that causes an object to change its movement from a "straight line" comes to us from Newton's laws. > Why does the existence of a transformation that makes movement under a supposed force…

Actually it's quite easy to cast electromagnetism into a purely geometrical form, you just add a few extra curled up dimensions to a flattish spacetime in general relativity and you basically get Maxwell's equations for free. There are other reasons that's not a great theory (IIRC sources and self-action get nasty and you have to make arbitrary choices about scale, etc), but it's straightforward to get force laws out of pure geometry.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#192

Post by Koshkin »

est31 wrote: post #55
Smaug123 wrote: post #43

Earlier quoted context omitted.

Good point; this becomes more obvious if you imagine throwing the ball up and then immediately collapsing all the mass of the Earth into a single point at the centre. What path does the ball follow now? It's probably following a path we would more usually call an "orbit", and it sure looks a lot like an ellipse. Now just put the mass of the Earth back where it was, and notice that the ball hits the ground before it c…

Despite both being conic sections, cutting up an ellipse won't yield you parabolas. An ellipse has two focal points to which the sum of the distances is constant, while a parabola has a focal point and a directrix line to which the difference of the distances is constantly 0. Two different things.

Isn’t a conic section made by cutting up, well, a cone?

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#194

Post by gpsx »

Smaug123 wrote: post #14

I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?" I'll answer this question as I understand it, but I only took four lectures of General Relativity before I gave it up in favour of computability and logic, so if there is a more intuitive and/or less wrong an…

It is much easier to think in two dimensions than three. If you picture the ball following a parabolic trajectory in space then you are really thinking in three dimensions here. It might be easier to think of throwing the ball straight up, after which it eventually falls straight back down. NOW plot this in two dimensions with one of the dimensions being time. As the original comment says, the scaling of the time dimension in seconds is not a good comparison to meters. Physicist like units where the speed of light is 1 (one). In these units, in our two dimensional space-time graph, the ball travels a very far distance while the change in our space dimension is still small. It is very close to straight line.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#195

Post by willis936 »

pdonis wrote: post #179
asdfasgasdgasdg wrote: post #109

Earlier quoted context omitted.

> Spherical mass can be replaced with a point mass I'm not a physicist, but that doesn't sound right. One example is that if you are inside of the sphere, at least some of the mass will be pulling you away from the point at its center. I think what you mean is that a point mass closely approximates a spherical mass, but the degree to which that is true becomes less and less the closer you get to the center. I don't t…

> if you are inside of the sphere, at least some of the mass will be pulling you away from the point at its center If the mass is spherically symmetric, this will not be the case; all of the Newtonian forces from the masses further away from the center than you are will cancel out. This is called the "shell theorem", and it turns out to hold even in General Relativity.

I don’t think this is correct. I think the shell theorem says that the gravitational forces cancel if you are on the inside of a hollow sphere and all mass is on the surface. A perfect sphere of uniform density would not meet the shell theorem assumptions.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#196

Post by Koshkin »

abhishekjha wrote: post #131
Ancapistani wrote: post #101

Earlier quoted context omitted.

I just had another thought. The word “dimension” in this context is overloaded. We think of space being three dimensions but really it’s only one - velocity relative to a specific reference frame. Thinking of it this way, the word “spacetime” makes sense; it’s a two-dimensional system: “spatial velocity” (S) on one axis and “temporal velocity” (T) on another. Both velocities are always measured against a reference fr…

By c do you mean the speed of light? How is it dimensionless?

Whether something is dimensionless is pure convention. By making c dimensionless and, for even more convenience, setting its value to 1, you can measure distance in seconds!

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#197

Post by gpsx »

sohkamyung wrote: post #36
Smaug123 wrote: post #14

I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?" I'll answer this question as I understand it, but I only took four lectures of General Relativity before I gave it up in favour of computability and logic, so if there is a more intuitive and/or less wrong an…

Off topic, but in reality, the trajectory of a ball thrown on Earth is not a parabola, but an ellipse [1]: > under the laws of gravity, a parabola is an impossible shape for an object that's gravitationally bound to the Earth. The math simply doesn't work out. If we could design a precise enough experiment, we'd measure that projectiles on Earth make tiny deviations from the predicted parabolic path we all derived in…

If you want to get technical, what about air resistance?

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#198

Post by srtjstjsj »

pdonis wrote: post #177
fouronnes3 wrote: post #66

Earlier quoted context omitted.

It's a parabola in a uniform gravity field, an ellipse in a circular gravity field coming from a point mass. So if you want to be really pedantic, it's never an ellipse because the Earth is not a point mass. It would be equivalent to a point mass if the Earth were a perfect sphere of uniform density, but it isn't. In reality it's a potato like mass blob that's approximated by what geodesists call the "geoid". So in o…

> It's a parabola in a uniform gravity field In relativity, there is no such thing as a "uniform gravity field", if by that you mean a field where the "acceleration due to gravity" is the same everywhere. The closest you can come is the "gravity field" inside a rocket accelerating in a straight line in empty space, where the acceleration felt by the crew is constant. That kind of "gravity field" has an "acceleration…

Why would acceleration not be constant? (Assuming the ship isn't moving from the center of the earth outward or something like that.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#199

Post by Koshkin »

Smaug123 wrote: post #27
paulpauper wrote: post #17

Earlier quoted context omitted.

>I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?" Air resistance, wind, and horizonal acceleration. Over long vertical distances, these perturbations in the x-axis cause an arc. Nothing to do with general relativity.

I assert that if you throw a ball upwards in a vacuum chamber on Earth, it will in fact still fly in a parabola.

Which is one reason scientists used to think that vacuum doesn’t exist.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#200

Post by drdeca »

colordrops wrote: post #98
gilgoomesh wrote: post #78

Earlier quoted context omitted.

The falling object doesn't accelerate. You, standing on the ground are the one that's accelerating. You see the object as accelerating but that's an illusion due to frames of reference. As evidence: which object feels a force on it? You can feel the force the ground continually pushes up at you. The ground is accelerating you up. The falling object is completely idle in its inertial frame and feels nothing.

Ok so that makes sense, but if we are accelerating by standing on the ground, isn't that implying that we are continuously increasing in energy? Couldn't that be harvested for a perpetual motion machine of some sort?

First, "it all adds up to normality". Second, hm, I'm not sure. Well, the glass on the table next to me is "accelerating", but in my frame of reference (which is the same as that of the glass) it is also stationary...?

If I drop a ball above the glass, and we consider things from the frame of reference where the ball is stationary, which (neglecting air resistance) is an inertial reference frame. In this frame, the glass is accelerating ball-wards , because of the table pushing on it, and, this force is applied over a distance as the glass approaches the ball. So, yes, it seems that the KE of the glass should be increasing in the reference frame of the ball.

Hm, I'm confused.

I suppose if we consider a geodesic representing a periodic orbit around the earth, that the positions and velocities of various objects on earth will be in a cyclic pattern?

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